# How do you simplify (\frac { 4} { 9} - \frac { 1} { 3} ) \div \frac { 7} { 10}?

Jan 16, 2018

See a solution process below:

#### Explanation:

First, execute the operation in parenthesis by putting the fractions over common denominators:

$\left(\frac{4}{9} - \left[\frac{3}{3} \times \frac{1}{3}\right]\right) \div \frac{7}{10} \implies$

$\left(\frac{4}{9} - \frac{3}{9}\right) \div \frac{7}{10} \implies$

$\left(\frac{4 - 3}{9}\right) \div \frac{7}{10} \implies$

$\frac{1}{9} \div \frac{7}{10}$

Next, we can rewrite the expression as:

$\frac{\frac{1}{9}}{\frac{7}{10}}$

Now, we can use this rule for dividing fractions to complete the simplification:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{1}}{\textcolor{b l u e}{9}}}{\frac{\textcolor{g r e e n}{7}}{\textcolor{p u r p \le}{10}}} \implies \frac{\textcolor{red}{1} \times \textcolor{p u r p \le}{10}}{\textcolor{b l u e}{9} \times \textcolor{g r e e n}{7}} \implies \frac{10}{63}$